Sunday, August 8, 2010

GET READY FOR THE NEXT LEVEL OF MATH

With the Fall semester right around the corner, conscientious students are starting to recognize that familiar “butterfly” feeling. What will my classes be like? What will I be expected to learn? to do? to know already?

It’s that last question that you can control. Be prepared to move forward in your next math class by reviewing what you already know. Here’s a handy list of concepts for the most frequently required math classes.

ELEMENTARY ARITHMETIC:
-- Start practicing adding, subtracting, multiplying, and dividing.
-- Practice multiplication tables and number families.

PRE-ALGEBRA:
-- Practice those computation skills so adding, subtracting, multiplying, and dividing are quick and easy for you. This will give you the mental space to learn the first concepts that will take you from arithmetic to mathematics.

ALGEBRA I:
-- Review last year’s work in Pre-Algebra if you still have it.
-- Ask the local library if there is a copy of the Algebra textbook on the shelf. It would probably be a reference copy, so you won’t be able to check it out. Make a photocopy of the Table of Contents and leaf through the first chapter which is frequently a review of past material.
-- Be prepared for these concepts:
COLLECT LIKE TERMS
SOLVE EQUATIONS WITH ONE VARIABLE
PROPERTIES OF REAL NUMBERS (Commutative, Associative, Distributive, Identify, Inverse, Reflexive, Transitive, Substitution)

GEOMETRY:
Do you want the good news first or the bad news? The good news is that there is very little in the average Geometry curriculum that you don’t already know. You’ve been learning a little Geometry every year since Kindergarten, which is the bad news. Some of the concepts you learned maybe 9 years ago and they may be buried under a lot of other stuff that you’ve learned in the interim. Start digging!
-- SHAPES -- square, rectangle, rhombus, parallelogram, trapezoid, circle, triangle. Know how to tell what each shape is (properties) and the equation for finding the area.
-- AREAS -- yes, I know I’ve mentioned that already, but it is a basic concept that causes trouble for many students. Know how to calculate areas and perimeters, too.
-- VOCABULARY -- The names of shapes is an example of vocabulary that you will be expected to already know. Add point-line-plane to the list, as well as diagonal, radius, diameter, arc, area, perimeter, volume (and related equations), Pythagorean Theorem, isosceles, equilateral, equiangular, skew, obtuse, acute, complementary, and supplementary. There may be more terms that you’ve already learned. Can you add to the list?
-- ALGEBRA -- “WHAT? I have to know last year’s Algebra in order to succeed in this year’s Geometry?” Yes. You’ll be asked to solve Geometry problems by using one-variable equations (like area) and systems of equations too. There may even be a few quadratic equations, so review factoring.
The biggest hint for success in your Geometry class is to learn the postulates and theorems well and as they are introduced.

ALGEBRA II:
-- Review your Algebra I notes from 2 years ago. If you haven’t developed the practice of filing notes from each class, resolve NOW to archive old class material now that you see how helpful it can be in future years.
-- Be prepared to factor quadratic equations and FOIL binomials.
-- Review the real number properties that allow you to solve equations.

TRIGONOMETRY:
Triangles are paramount shapes in Trig, so review everything you've learned about them. Pythagorean Theorem will have new applications and SohCahToa with be the basis for learning 3 more side relationships. A little review of circles will be helpful in the first couple of weeks when you're introduced to the Unit Circle.
A huge hint for success in Trig is to learn the Unit Circle when told to do so. You can expect to be tested on it in a stringent, timed format. After enough time to forget what you've memorized, you'll be expected to actually USE the information, so try to find patterns in the angles and the sine, cosine, and tangent values. This strategy will help you access the information in later problems.

PRECALCULUS:
Factoring is a stumbling block for even some high ability students. Practice it until you could "factor in your sleep." Review graphs of second and third degree equations, square roots, absolute value, and rational equations. A quick review of your old Algebra II work can help you to recall concepts you learned previously. Much of Precalc will be an exercise in deeper analysis of these same concepts.

IN GENERAL:
Check out older blogs for more detailed tips for each class.

GOOD LUCK!
Not everyone is as excited about the beginning of a new semester as I am, but I know for sure that success in the first few weeks of school can lay the groundwork for a productive course and a good grade. My goal is for YOU to be the first student in the class to answer a question correctly. I want the teacher to go home that night believing that YOU are the best student ever. My experience shows that this can become a self-fulfilling prophesy that can enhance your classroom and exam performance.